Beamforming codebook generation system and associated methods

ABSTRACT

A codebook generation system and associated methods are generally described herein. For instance, a codebook generation agent (CGA) may implement techniques for generating one or more matrix codebooks from vector codebooks. The CGA may be implemented in mobile devices (e.g., stations, subscriber units, handsets, laptops, etc.). In this regard, the dynamic generation of matrix codebooks rather than having them stored on the mobile device enables the mobile device to utilize the memory normally consumed by the matrix codebooks in support of other features and/or services.

RELATED APPLICATIONS

This application is a continuation-in-part application of applicationSer. No. 11/036,906 filed Jan. 13, 2005 of the same title, inventor andcommonly assigned to Intel, Corporation.

TECHNICAL FIELD

Embodiments of the invention are generally directed to communicationsystems and, more particularly, to a codebook generation system andassociated methods.

BACKGROUND

Closed loop multiple-input-multiple-output (MIMO) systems typicallytransmit channel state information from a receiver to a transmitter.Transmitting the channel state information consumes bandwidth that mightotherwise be available for data traffic.

Illustratively, conventional frequency division duplex (FDD) systemsthat employ beamforming (or, closed loop multiple input, multiple output(MIMO), the beamforming matrix (referred to herein as a codeword)generated in response to perceived channel conditions is computed andquantized at the receiver first, and then is provided to the sourcetransmitter (e.g., via feedback). A conventional approach to reduce theoverhead associated with this feedback is to provide matrix codebook(s)at each of the transmitter and the receiver, each of the codebook(s)comprising a plurality, or set, of potential beamforming matrixes thatmay be used depending on the channel conditions perceived at thereceiver. When the receiver has identified the appropriate matrixcodebook(s), the receiver will typically feed back only an index(instead of the actual matrix entries) that points to the appropriatecodeword in the codebook(s) stored at the transmitter.

Thus, for a different combination of transmit antenna(e) (N_(t)) anddata streams (N_(s)), a different matrix codebook is required.Conventionally, the size of the codebook is based on the number oftransmit antennae and the number of data streams: N_(t)×N_(s). For somesystems, e.g., one implementing the developing 802.16e¹, N_(t) and N_(s)are currently less than five (5) but are likely to increase to eight(8). Therefore, a substantial number of N_(t) by N_(s) combinations areanticipated, requiring a significant amount of memory within mobilecommunication devices in order to store such a large number ofcodebooks. ¹ See, e.g., the ANSI/IEEE Std 802.16-2001 Standard for Localand Metropolitan area networks Part 16: Air Interface for FixedBroadband Wireless Access Systems, its progeny and supplements thereto(e.g., 802.16a, .16d, and .16e).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention are illustrated by way of example,and not by way of limitation, in the figures of the accompanyingdrawings in which like reference numerals refer to similar elements andin which:

FIG. 1 is a block diagram of an example communication system withinwhich embodiments of the invention may be practiced;

FIG. 2 is a flow chart of an example method for generating codebook(s),according to one embodiment;

FIG. 3 provides a graphical representations of the performance ofembodiments of the invention versus a conventional techniques;

FIG. 4 is a block diagram of an example communications deviceincorporating one or more embodiments of the invention; and

FIG. 5 is a block diagram of an example article of manufacture includingcontent which, when executed by an accessing machine, causes the machineto implement one or more aspects of embodiment(s) of the invention.

DETAILED DESCRIPTION

Embodiments of a codebook generation system and associated methods aregenerally presented. According to one embodiment, described more fullybelow, a codebook generation agent (CGA) is presented which mayimplement a method for generating one or more matrix codebooks fromvector codebooks.

According to one embodiment, the CGA is implemented in mobile devices(e.g., stations, subscriber units, handsets, laptops, etc.), althoughthe invention is not limited in this regard. As developed more fullybelow, the CGA may develop one or more matrix codebook(s) from matrixcodewords that are dynamically generated from vector codebook(s) for 2-,3-, 4-, . . . , N-unit vectors already resident on the device in supportof other features (e.g., single data stream beamforming). In thisregard, the use of the vector codebook(s) for 2-, 3- and 4-unit vectorsdoes not add any extra complexity or memory drain to the mobile device.On the contrary, by dynamically generating the matrix codebooks ratherthan having them stored on the mobile device, enables the mobile deviceto utilize the memory normally consumed by the matrix codebooks insupport of other features and/or services.

More particularly, as developed more fully below, the CGA may implementone or more of four (4) disclosed techniques for generating the matrixcodebooks. According to some embodiments, the codebook generation agentmay leverage the Householder reflection and an appropriate one or morevector codebook(s) of 2-, 3- and/or 4-unit vector to generate one ormore suitable matrix codeword(s) for compilation into a matrix codebookfor a given set of channel conditions.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

Technical detail regarding some of the operating characteristics of themobile devices and/or the wireless communication network(s) in which theCGA may be implemented may be found in, e.g., the IEEE 802.11, 1999Edition; Information Technology Telecommunications and InformationExchange Between Systems—Local and Metropolitan Area Networks—SpecificRequirements, Part 11: WLAN Medium Access Control (MAC) and Physical(PHY) Layer Specifications, its progeny and supplements thereto (e.g.,802.11a, .11g and. 11n). See, also, the IEEE Std 802.16-2001 IEEE Std.802.16-2001 IEEE Standard for Local and Metropolitan area networks Part16: Air Interface for Fixed Broadband Wireless Access Systems, itsprogeny and supplements thereto (e.g., 802.16a, .16d, and .16e).

Example Communications Environment

In FIG. 1, a block diagram of an example wireless communicationenvironment 100 is depicted within which embodiments of the inventionmay well be practiced. In accordance with the illustrated exampleembodiment of FIG. 1, an example communications environment 100 isdepicted comprising one wireless communications device 102 incommunication with another wireless communications device 106 through awireless communication link 104. As used herein, communicationenvironment 100 is intended to represent any of a wide range of wirelesscommunication networks including, but not limited to, a near-fieldcommunication (NFC) network, a wireless local area network (WLAN), awireless metropolitan area network (WMAN), a cellular radiotelephonynetwork, a personal communication system (PCS) network, and the like.

According to one embodiment, communication network 100 is an 802.16xcommunication network, and device 102 is a base station while device 106is a subscriber station, although the scope of the invention is notlimited in this regard. In a closed-loop MIMO (or, as above, abeamforming system) the data signal is first weighted by a beamformingmatrix V, and then selectively transmitted by a plurality of antennae,as shown. According to one embodiment, the data signal may comprise anumber of data streams (N₁ . . . N_(s)), although the invention is notlimited in this regard. The number of data streams may represent thenumber of spatial channels, with appropriate bit-loading, powerweighting and subcarrier assignments, although the invention is notlimited in this regard.

According to one embodiment, with four (4) transmit antennae and three(3) data streams (for ease of illustration), the transmitted signal (x)transmitted via the N_(t) antennae may be represented as:

$\begin{matrix}{{x = {V \times s}}{where}{{V = \begin{bmatrix}v_{11} & v_{12} & v_{13} \\v_{21} & v_{22} & v_{23} \\v_{31} & v_{32} & v_{33} \\v_{41} & v_{42} & v_{43}\end{bmatrix}},{{{and}\mspace{14mu} s} = \begin{bmatrix}s_{3} \\s_{2} \\s_{3}\end{bmatrix}}}} & (1)\end{matrix}$As shown, s is an N_(s)-vector of data symbols, and V is the N_(t) byN_(s) beamforming matrix developed from information (e.g., matrixcodebook(s) and or indices thereto) fed back from a remote receiver.According to one embodiment, the beamforming matrix V is typicallyunitary, and power/bit loading is applied on vector s, as introducedabove.

Device 106 is depicted comprising a codebook generation agent (CGA) 108to dynamically generate one or more matrix codebook(s) from whichchannel state information may; be characterized and fed back to the basestation, 102. As introduced above, rather than storing one or morematrix codebooks, CGA 108 compiles the matrix codebooks necessary tocharacterize the channel state information from matrix codeword(s)dynamically generated from one or more vector codebook(s) for 2-, 3-,4-, . . . , N-unit vectors. As discussed more fully below, the vectorcodebook(s) are recursively applied to a suitable transform (e.g., aHouseholder reflection) from the lowest-order codebook to the highestorder codebook, as necessary to generate the desired size matrixcodeword(s) from which the matrix codebook(s) are assembled.

It will be appreciated that but for the introduction of the CGA 108,device 106 is intended to represent any of a wide variety of electronicdevice(s) with wireless communication capability. In some embodiments,CGA 108 may well be implemented within a receiver element of a device.In other embodiments, CGA 108 is responsive to a communicatively coupledreceiver to perform the functions described herein. According to someembodiments, CGA 108 may well be implemented in hardware, software,firmware and/or any combination thereof.

Example Operation

As introduced above, CGA 108 may generate the matrix codebook(s) fromthe one or more vector codebooks according to a number of techniques,each described more fully below. The first technique disclosed offersthe closest approximation to the conventional technique of using storedmatrix codebooks. The second through fourth technique disclosed alsooffer very good results, although with decreased computationalcomplexity. In either case, the computational complexity is more thanoffset by the reduced memory that need be allocated to the storage ofthe matrix codebooks.

Turning to FIG. 2, a flow chart of an example method for dynamicallygenerating one or more matrix codebook(s) is generally presented,according to one embodiment. As shown, the method begins with block 202by dynamically identifying the size of the matrix codeword(s) required.More particularly, according to one embodiment CGA 108 disposed within,or otherwise responsive to a receiver (e.g., 106) may be invoked todetermine the size of the matrix codebook necessary. According to oneembodiment, the size of the codeword required is dependent upon thenumber of transmit antennae (N_(t)) and/or the number of spatial datastreams (N_(s)) utilized in the communication channel, although otherparameters may be considered as a supplement to, or in place of, N_(t)and/or N_(s). According to one embodiment, the necessary parameters areeither supplied to, or perceived by the receiver and/or CGA 108 for usein determining the size of the matrix codeword to generate.

As shown, CGA 108 is depicted comprising vector codebooks for 2-, 3-,4-, . . . , N-unit (or, parameter) vectors. Accordingly, CGA 108dynamically selects the vector codebook(s) suitable for a particularelement of the recursive process for generating an element of the matrixcodeword(s), as provided more fully below.

In response to determining the necessary size of the matrix codeword,CGA 108 may dynamically select an appropriate one or more vectorcodebook(s) suitable for generating at least an element of the matrixcodeword, block 204. According to one embodiment, the vector codebook(s)selected by CGA 108 may depend on which of the techniques will beemployed to generate the matrix codeword(s). According to oneembodiment, the technique to be used is dynamically selected by CGA 108and may depend on any of a number of factors including, but not limitedto, the current processing load of the receiver and/or CGA 108, theperceived quality of the channel, and the like. That is, the currentprocessing load of the receiver and/or CGA 108 may be such that a lowercomplexity codebook generation technique is required. Similarly, if theperceived quality of the channel (e.g., through signal-to-noise ratio,received power level, etc.) is high, CGA 108 may determine that a lowercomplexity codebook generation technique will provide suitable results,whereas a poorer channel may benefit from use of a more complextechnique that more closely approximates the use of conventional(stored) codebooks.

Once the matrix codebook is generated, conventional techniques forcomputation and quantization of the proposed beamforming matrix may beemployed, such as the one described in co-pending U.S. patentapplication Ser. No. 10/937,097 entitled Recursive Reduction of ChannelState Feedback by Li, et al., commonly assigned to the Assignee of thisapplication, and incorporated by reference herein for all purposes.

Returning to block 206, as provided above CGA 108 may employ one or moreof at least four (4) techniques for recursively generating one or morematrix codeword(s) from vector codebook(s) for 2-, 3-, 4-, . . . N-unitvectors. It will be appreciated that other techniques for generating amatrix codeword from vector codebooks may well be used without deviatingfrom the scope and spirit of the claims, below. Each of the fourtechniques are presented, as follows.

Technique 1

According to one embodiment, CGA 108 may generate a matrix codeword,column by column, using vector codebooks starting from the smallestdimension of the matrix codeword and working towards the largestdimension. For example, to generate a 4×3 matrix codeword, CGA 108 mayemploy unit vectors of dimensions 2, 3, and 4 sequentially, startingfrom the most inner-most parentheses (or, lowest dimension) and workingout towards higher dimensions of the codeword, as shown:

${V\mspace{11mu}( {l_{N_{t}},\ldots\mspace{11mu},l_{N_{t} - N_{s} + 1}} )} = {\quad{P_{N_{t}}{\quad{{\begin{matrix}\begin{bmatrix}1 & {\mspace{14mu}{0\mspace{70mu}\cdots\mspace{95mu} 0}} \\\begin{matrix}\begin{matrix}0 & \; \\\vdots & P_{N_{t} - 1}\end{matrix} \\\; \\{0\mspace{79mu}}\end{matrix} & \begin{bmatrix}1 & ⋰ & {\mspace{45mu} 0} \\\begin{matrix}0 \\\vdots \\0\end{matrix} & P_{N_{t} - N_{s} + 2} & \begin{bmatrix}1 & 0 \\\begin{matrix}0 \\\vdots \\0\end{matrix} & {v_{N_{t} - N_{s} + 1}( l_{N_{t} - N_{s} + 1} )}\end{bmatrix}\end{bmatrix}\end{bmatrix}\end{matrix}\mspace{20mu} P_{i}} = {{I - {\frac{2}{{w^{H}w}}w\; w^{H}\mspace{20mu} w}} = {{{\mathbb{e}}^{- {j\phi}_{i,1}}{v_{i}( l_{i} )}} - e_{1}}}}}}}$In the special case, v_(i)=e₁, the householder reflection can becomputed as. P_(i)=I. Without unnecessary repetition, it is understoodthat this special treatment is implied in all the following description.

The N_(t) by N_(s) matrix codeword is constructed from the last columnrecursively, where the iteration starts from the lower, right hand sidecorner. Successive iteration(s) adds one column and one row to theconstructing matrix codeword. In this regard, let {v_(i)(l_(i))}_(l)_(i) ₌₁ ^(L) _(i) denote the codebook of i-dimension unit vectors withL_(i) codewords (i.e. vectors), where l_(i) is the codeword index. Let{v_(t)(l_(t))}_(l) _(t) ₌₁ ^(L) _(i) ={1}, i.e. v₁(1)=1 and L₁=1. Let{V_(N) _(t) _(×N) _(s) (l)}_(l=1) ^(L) denote the matrix codebook ofdimension N_(t) by N_(s) with L codewords, where

$L = {\prod\limits_{i = 1}^{N_{s}}\;{L_{i}.}}$The matrix codebook {V_(N) _(t) _(×N) _(s) (l)}_(l=1) ^(L) can beconstructed by N_(s) vector codebooks according to the followingpseudo-code:

I.  FOR  l_(N_(t) − N_(s) + 1) = 1 : L_(N_(t) − N_(s) + 1) I.1. IfN_(t) > N_(s)I.1.1.       V_(t) = v_(N_(t) − N_(s) + 1)(l_(N_(t) − N_(s) + 1))I.2. ELSE I.2.1.   V_(t) = 1 I.3. ENDII.  FOR   l_(N_(t) − N_(s) + 2) = 1 : L_(N_(t) − N_(s) + 2)II.1.  w = e^(−j ϕ_(l))v_(N_(t) − N_(s) + 2)(l_(N_(t) − N_(s) + 2)) − e₁,$\begin{matrix}{{where}\mspace{14mu}\phi_{1}\mspace{11mu}{is}\mspace{14mu}{the}\mspace{14mu}{phase}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{first}} \\{{entry}\mspace{14mu}{of}\mspace{14mu}{v_{N_{t} - N_{s} + 2}( l_{N_{t} - N_{s} + 2} )}\mspace{14mu}{and}}\end{matrix}\quad$ e₁ = [1, 0 . . . 0]^(T).${{II}{{.2}.\mspace{14mu} P_{N_{t} - N_{s} + 2}}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$${{II}{{.3}.\mspace{14mu} V_{t}}} = {P_{N_{t} - N_{s} + 2}\begin{bmatrix}1 & 0 \\0 & V_{t}\end{bmatrix}}$III.  FOR  l_(N_(t) − N_(s) + 3) = 1 : L_(N_(t) − N_(s) + 3) . . .     .. . N_(s).  FOR  l_(N_(t)) = 1 : L_(N_(t))N_(s).1.    w = e^(−j ϕ_(l))v_(N_(t))(l_(N_(t))) − e₁,where  ϕ₁  is  the  phase  of  the  first  entry  of  v_(N_(t))(l_(N_(t))).${N_{s}{{.2}.\mspace{25mu} P_{N_{t}}}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$${{N_{s}{{.3}.\mspace{25mu}{V(l)}}} = {P_{N_{t}}\;\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & \; & V_{t} & \; \\0 & \mspace{11mu} & {\;.} & \;\end{bmatrix}}},$${{where}\mspace{14mu} l} = {l_{N_{t}} + {\sum\limits_{i = {N_{t} - N_{i} + 1}}^{N_{t} - 1}{l_{i}{\prod\limits_{j = {i + 1}}^{N_{t}}\; L_{j}}}}}$N_(s).4.   END . . .     . . . II.4. END I.4. END

As shown above, CGA 108 may generate a matrix from the most inner corewith the smallest dimension (the lowest dimension) to the full matrix.The lowest dimension core is either 1, or a vector of sizeN_(t)−N_(s)+1. Each expansion, or recursive iteration, effectivelyincreases the size of the matrix by one row and one column. There are NsFOR loops for Nt>Ns, and there are Nt−1 FOR loops for Nt=Ns. Each FORloop corresponds to one expansion of the matrix codeword, each expansiongenerally comprising:

1) picking an appropriate vector from the vector codebook;

2) removing the phase of the first element of the vector by e^(−jφ) _(l)v_(N) _(t) (l_(N) _(t) ) and subtract one from the first element of thephase corrected vector w=e^(−jφ) _(t) v_(N) _(t) (l_(N) _(t) )−e₁;

3) generating a Householder matrix

${P = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}};$

4) padding zeros and a one in the previous expanded matrix V as

$\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & \; & V_{t} & \; \\0 & \; & \; & \;\end{bmatrix};$and

5) multiplying the Householder matrix with the padded matrix to finishone expansion.

Since the vector steps through the vector codebook, the number of runsfor each FOR loop is equal to the number of vectors in the correspondingvector codebook. The index l is the index for the matrix finallygenerated. It increases as 1, 2, . . . , L_(Nt)*L_(Nt−1) . . .*L_(Nt−Ns+1), where L_(t) is the number of vectors in the vectorcodebook of dimension t.

To reduce complexity and speed up computation, the phase of the firstentry of each vector may be removed when CGA 108 stores each vectorcodebook as e^(−jφ) _(t) v_(N) _(t) (l_(N) _(t) ). Namely, each firstelement of each vector in each vector codebook is real (not complex).The real number

$\frac{2}{{w^{H}w}}$may also be pre-computed and stored for each vector.Technique 2

According to one embodiment, CGA 108 may well implement a secondtechnique to generate one or more matrix codeword(s) from vectorcodebook(s) for 2-, 3-, 4-, . . . N-unit vectors. In this technique, CGA108 employs the complementary property of unitary matrix as follows.Instead of generating a N_(t) by N_(s) matrix directly, it firstgenerates a N_(t) by N_(t) matrix first and then cut a submatrix ofdimension N_(t) by N_(s) from it.

This technique is the most efficient when it generates matrix codebookof dimension N_(t) by (N_(t)−1). As specified above, the storedN_(t)-vector codebook has the property that the N_(t)-vector codewordsare spread over the complex N_(t)-sphere as uniformly as possible, wherethe minimum angle between any two vectors is maximized. Note that eachvector has a complementary, orthogonal subspace, spanned by (N_(t)−1)orthogonal vectors, and is orthogonal to the vector. The property of thevector codebook implies that the subspaces (i.e. N_(t) by (N_(t)−1)matrixes) are uniformly spread, where the minimum angle between any twosubspaces is maximized. This maximum minimum angle is a desirableproperty for N_(t) by (N_(t)−1) matrix codebook. The major advantage ofscheme 2 is that only one vector codebook is required to generate theN_(t) by (N_(t)−1) codebook, while (N_(t)−1) vector codebooks arerequired in Technique 1.

Technique 2 is also efficient to generate matrix codebook of dimensionN_(t) by N_(s), where

$N_{s} > {\frac{N_{t}}{2}.}$For this case, the CGA 108 first generates an N_(t)×N_(t) matrix, andthen cuts a N_(t) by N_(s) submatrix from it as a matrix codeword. Thepseudo code of the scheme is as follows, where the notations are alreadydefined, above, in Technique 1. It is assumed that

$N_{s} > {\frac{N_{t}}{2}.}$One advantage of this scheme is that only N_(t)−N_(s) vector codebooksare required to generate the N_(t)×N_(s) codebook, while N_(s) vectorcodebooks may be required for Technique 1.

I.  FOR  l_(N_(s) + 1) = 1 : L_(N_(s) + 1)I.1.    w = e^(−j ϕ_(l))v_(N_(s) + 1)(l_(N_(s) + 1)) − e₁$\begin{matrix}{{where}\mspace{14mu}\phi_{1}\mspace{11mu}{is}\mspace{14mu}{the}\mspace{14mu}{phase}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{first}} \\{{{entry}\mspace{14mu}{of}\mspace{14mu}{v_{N_{t} - N_{s} + 2}( l_{N_{t} - N_{s} + 2} )}\mspace{14mu}{and}\mspace{14mu} e_{1}} = {\lbrack {1,{0\mspace{11mu}\ldots\; 0}} \rbrack^{T}.}}\end{matrix}$${I{{.2}.\mspace{25mu} V_{t}}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$II.  FOR  l_(N_(s) + 2) = 1 : L_(N_(s) + 2)I I.1.    w = e^(−j ϕ_(l))v_(N_(s) + 2)(l_(N_(s) + 2)) − e₁,$\begin{matrix}{{where}\mspace{14mu}\phi_{1}\mspace{11mu}{is}\mspace{14mu}{the}\mspace{14mu}{phase}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{first}} \\{{{entry}\mspace{14mu}{of}\mspace{14mu}{v_{N_{s} + 2}( l_{N_{s} + 2} )}\mspace{14mu}{and}\mspace{14mu} e_{1}} = {\lbrack {1,{0\mspace{11mu}\ldots\mspace{14mu} 0}} \rbrack^{T}.}}\end{matrix}$${{II}{{.2}.\mspace{25mu} P_{N_{s} + 2}}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$${{II}{{.3}.\mspace{14mu} V_{t}}} = {P_{N_{s} + 2}\begin{bmatrix}1 & 0 \\0 & V_{t}\end{bmatrix}}$ III.  FOR  l_(N_(s) + 3) = 1 : L_(N_(s) + 3) . . .    .. . N_(s).   FOR  l_(N_(t)) = 1 : L_(N_(t))N_(s).1.    w = e^(−j ϕ_(l))v_(N_(t))(l_(N_(t))) − e₁,where  ϕ₁  is  the  phase  of  the  first  entry  of  v_(N_(t))(l_(N_(t))).${N_{s}{{.2}.\mspace{14mu} P_{N_{t}}}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$${N_{s}{{.3}.\mspace{25mu} V_{t}}} = {{P_{N_{t}}\;\begin{bmatrix}1 & 0 & \ldots & 0 \\0 & \; & \; & \; \\\vdots & \; & V_{t} & \; \\0 & \mspace{11mu} & \; & \;\end{bmatrix}}.}$ N_(s).4. V(l) = last N_(s) columns of V_(t),${{where}\mspace{14mu} l} = {l_{N_{t}} + {\sum\limits_{i = {N_{s} + 1}}^{N_{t} - 1}{l_{i}{\prod\limits_{j = {i + 1}}^{N_{t}}\; L_{j}}}}}$N_(s).5. END . . .    . . . II.4. END I.3. ENDTechnique 3

According to one embodiment, CGA 108 may well implement a thirdtechnique to generate one or more matrix codeword(s) from vectorcodebook(s) for 2-, 3-, 4-, . . . N-unit vectors. This techniquerepresents a further simplification over technique 2, above. For thegeneration of an N_(t) by (N_(t)−1) codebook, techniques 2 and 3 arevery similar in terms of computational complexity. However, whengenerating an N_(t) by N_(s) codebook with L codewords, this thirdtechnique provides for the use of only one vector codebook with Lcodewords and span each vector into a N_(t) by N_(t) matrix usingHouseholder reflection. The N_(t) by N_(s) matrix codebook is formed bytaking a N_(t) by N_(s) submatrix from each spanned N_(t) by N_(t)matrix. Example pseudo code of for technique 3 is as follows:

1. FOR l = 1:L 2.    w = e^(−j ϕ_(l))v_(N_(t))(l) − e₁ $\begin{matrix}{{where}\mspace{14mu}\phi_{1}\mspace{11mu}{is}\mspace{14mu}{the}\mspace{14mu}{phase}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{first}\mspace{14mu}{entry}\mspace{14mu}{of}\mspace{14mu}{v_{N_{t}}(l)}\mspace{14mu}{and}} \\{e_{1} = {\lbrack {1,{0\mspace{11mu}\ldots\; 0}} \rbrack^{T}.}}\end{matrix}\quad$${3.\mspace{14mu} V_{t}} = {I - {\frac{2}{{w^{H}w}}w\; w^{H}}}$4.  V(l) = last N_(s) columns of V_(t) 5. ENDTechnique 4

According to one embodiment, CGA 108 may employ yet a fourth techniqueto generate matrix codeword(s) from vector codebook(s) for 2, 3, 4 . . .N-unit vectors, according to one embodiment. According to oneembodiment, the fourth technique represents a further simplification oftechnique three, above. In particular, in step 4 of technique 3, CGA 108may take any N_(s) columns of Vt, such as the first N_(s) columns, orN_(s) columns extracted for the N_(t) columns.

It should be appreciated that combinations of techniques 1-4 arepossible, without deviating from the scope and spirit of the invention.For example, techniques 1 and 2 expand the matrix from a small core to abig matrix iteratively as shown above. According to one embodiment, thesmall core (or, lowest dimension) may be generated using othertechniques. For example, to generate a 4×3 matrix, the core (lowestdimension) used in technique 1 may be generated by technique 3. In thisregard, CGA 108 may use technique 3 to generate a core matrix of size3×2 using a 3-vector codebooks, and then use the remaining teachings oftechnique 1 to finish the generation of 4×3 using the 3×2 core as thelowest dimension.

To illustrate the algorithm, we use an example of 3/6 bits vectorcodebooks to generate all the necessary matrix codebooks. In 802.16e, itmay be desirable to implement codebooks, whose size L=3n bits, where nis integer.

Since there are many combinations of N_(t), N_(s), and L and each ofthem requires a corresponding codebook, the storage of all codebooks areburdensome. A set of codebooks is proposed, which can be dynamicallygenerated with low complexity.

For small size codebooks, i.e. 2×1, 3×1, and 4×1 with 3 bit index, threeoptimized, random codebooks are stored. For 3×1 and 4×1 with 6 bitindex, two structured codebooks are proposed, which can be dynamicallygenerated using an improved Hochwald method. For all the other matrixcodebooks such as 3×2 and 4×2, structured codebooks are proposed, whichcan also be dynamically generated with low complexity.

An example of stored vector codebooks for 2×1, 3×1, 4×1 with 3 bitindex, and 2×1 with 6 bit index are listed below in Table 1, Table 2,Table 3, and Table 4. The notation v(N_(t), N_(s), L) denotes the matrixcodebook (i.e. the set of complex unitary matrixes), which consists of2^(L) unit matrixes of a dimension N_(t) by N_(s). The number L is thenumber of bits required for the feedback index that can indicate anyvector in the codebook.

TABLE 1 v(2, 1, 3) Vector index 1 2 3 4 5 6 7 8 ν₁ 1 0.794 0.794 0.7940.794 0.329 0.511 0.329 ν₂ 0 −0.580 + 0.182i 0.058 + 0.605i −0.298 −0.530i 0.604 + 0.069i 0.661 + 0.674i 0.475 − 0.716i −0.878 − 0.348i

TABLE 2 v(3, 1, 3) Vector index 1 2 3 4 5 6 7 8 ν₁ 1 0.500 0.500 0.5000.500 0.495 0.500 0.500 ν₂ 0 −0.720 − 0.313i −0.066 + 0.137i −0.006 +0.653i   0.717 + 0.320i 0.482 − 0.452i 0.069 − 0.139i −0.005 − 0.654i ν₃0   0.248 − 0.268i −0.628 − 0.576i   0.462 − 0.332i −0.253 + 0.263i0.296 − 0.480i 0.620 + 0.585i −0.457 + 0.337i

TABLE 3 v(4, 1, 3) Vector index 1 2 3 4 5 6 7 8 ν₁ 1 0.378 0.378 0.3780.378 0.378 0.378 0.378 ν₂ 0 −0.270 − 0.567i   −0.710 + 0.133i 0.283 −0.094i −0.084 + 0.648i 0.525 + 0.353i 0.206 − 0.137i   0.062 − 0.333i ν₃0 0.596 + 0.158i −0.235 − 0.147i 0.070 − 0.826i   0.018 + 0.049i 0.412 +0.183i −0.521 + 0.083i   −0.346 + 0.503i ν₄ 0 0.159 − 0.241i   0.137 +0.489i −0.280 + 0.049i   −0.327 − 0.566i 0.264 + 0.430i 0.614 − 0.375i−0.570 + 0.211i

TABLE 4 v(2, 1, 6) Vector index 1 2 3 4 5 6 7 8 ν₁ 1 0.9744 0.97430.9743 0.9741 0.9739 0.9321 0.9320 ν₂ 0 0.2035 − j0.0961 −0.2250 −j0.0050 −0.0621 + j0.2166 0.1822 + j0.1340 0.0022 − j0.2268 −0.2925 +j0.2136 −0.2243 − j0.2847

TABLE 5 v(2, 1, 6) (cont'd) Vector index 9 10 11 12 13 14 15 16 ν₁0.9208 0.9207 0.9127 0.9048 0.8992 0.8972 0.8694 0.8629 ν₂ 0.3890 +j0.0303 0.2238 − j0.3196 0.2039 + j0.3542 −0.4083 − j0.1212 −0.0783 +0.0093 − 0.4479 − 0.4307 + j0.4305 j0.4416 j0.2085 j0.2645

TABLE 6 v(2, 1, 6) (cont'd) Vector index 17 18 19 20 21 22 23 24 ν₁0.8603 0.8436 0.8361 0.8221 0.8218 0.8160 0.8094 0.7886 ν₂ −0.4974 +j0.1120 −0.3229 + j0.4291 −0.2299 − j0.4980 0.1186 + −0.4533 − 0.2462 −0.5844 + −0.6044 − j0.5569 j0.3452 j0.5229 j0.0586 j0.1135

TABLE 7 v(2, 1, 6) (cont'd) Vector index 25 26 27 28 29 30 31 32 ν₁0.7757 0.7741 0.7737 0.7618 0.7556 0.7252 0.7194 0.6907 ν₂ 0.3859 +j0.4993 −0.0058 − j0.6330 −0.1463 + j0.6164 −0.5536 + 0.4976 − 0.6112 +0.6705 − −0.4194 + j0.3364 j0.4259 j0.3170 j0.1815 j0.5891

TABLE 8 v(2, 1, 6) (cont'd) Vector index 33 34 35 36 37 38 39 40 ν₁0.6842 0.6828 0.6762 0.6744 0.6657 0.6343 0.6156 0.6129 ν₂ −0.2715 −j0.6769 −0.7221 + j0.1111 0.2196 + j0.7032 −0.5482 − 0.3454 − −0.7415 −0.5315 + 0.0320 − j0.4946 j0.6615 j0.2187 j0.5819 j0.7895

TABLE 9 v(2, 1, 6) (cont'd) Vector index 41 42 43 44 45 46 47 48 ν₁0.6128 0.5915 0.5837 0.5645 0.5466 0.5173 0.5119 0.5018 ν₂ −0.1037 +j0.7834 −0.6850 + j0.4254 0.6336 − j0.5078 0.7888 + 0.8211 − −0.4757 −−0.4493 + −0.8626 + j0.2432 j0.1643 j0.7114 j0.7322 j0.0643

TABLE 10 v(2, 1, 6) (cont'd) Vector index 49 50 51 52 53 54 55 56 ν₁0.4938 0.4780 0.4562 0.4281 0.4259 0.3921 0.3822 0.3761 ν₂ 0.2917 +j0.8192 0.3911 − j0.7865 −0.7982 − j0.3934 0.6905 + j0.5831 −0.0806 −−0.7794 + 0.7782 − 0.9220 + j0.9012 j0.4887 j0.4983 j0.0917

TABLE 11 v(2, 1, 6) (cont'd) Vector index 57 58 59 60 61 62 63 64 ν₁0.3716 0.3080 0.2816 0.2568 0.2346 0.1951 0.1653 0.0866 ν₂ −0.1199 +−0.5759 − −0.9571 − 0.3374 − 0.4811 + −0.5888 + 0.9768 − −0.6811 −j0.9206 j0.7573 j0.0684 j0.9057 j0.8447 j0.7844 j0.1362 j0.7271

According to one embodiment, CGA 108 may generate matrix codebooks formultiple stream transmission from the vector codebooks in the previoussection using three operations depicted below. We assume that all unitvectors in the section are complex with unit norm and the first entry ofeach vector is real. The first operation is called Householderreflection transformation. It is to generate a unitary N by N matrixH(v) using a unit N vector v as:

$\begin{matrix}{{H\mspace{11mu}(v)} = \{ {\begin{matrix}{I,} & {v = e_{1}} \\{{I - {p\; w\; w^{H}}},} & {otherwise}\end{matrix},} } & (2)\end{matrix}$where w=v−e₁ and

${e_{1} = \lbrack {1\mspace{14mu} 0\mspace{14mu}\ldots\mspace{14mu} 0} \rbrack^{T}};{p = \frac{2}{{w^{H}w}}}$and it is a real number that can be pre-computed and stored for eachvector in the tables; I is the N by N identity matrix; ^(H) denotes theconjugate transpose operation.

The other two operations are built on Householder transformation. One ofthem is called H-concatenation, and the other is called H-expansion,where the “H” stands for Householder. The H-concatenation (HC) generatesa N by M+1 unitary matrix from a unit N vector and a unitary N−1 by Mmatrix using Householder transformation as

$\begin{matrix}{{{{HC}( {v_{N},A_{{({N - 1})} \times M}} )} = {{H( v_{N} )}\begin{bmatrix}1 & 0 & \cdots & 0 \\0 & \; & \; & \; \\\vdots & A_{{({N - 1})} \times M} & \; & \; \\0 & \; & \; & \;\end{bmatrix}}},} & (3)\end{matrix}$where N−1≧M ; the N−1 by M unitary matrix has property A^(H)A=I. Sinceboth terms on the left are unitary the output of HC is a unitary matrix.The H-expansion (HE) generates a N by M matrix from a unit N vector,v_(N), by taking the last M columns of H(v) asHE(v _(N) , M)=H(v _(N))_(:,N−M+1:N),   (4)CGA 108 may selectively employ one or more of the operations defined in(2), (3), and (4) to jointly generate matrix codebooks as follows. Intable 5, use of the nomenclature L bit codebook is intended to representthat the codebook has 2^(L) matrixes, which requires an L bit feedbackindex.

TABLE 5 Construction operations for N_(t) by N_(s) beamforming matrixwith 3, 6, and 9 bit codebooks. N_(s) N_(t) 2 3 4 2 antennas, H(v(2, 1,3)) 3 bit codebook 3 antennas, HE(v(3, 1, 3), 2) H(v(3, 1, 3)) 3 bitcodebook 4 antennas, HE(v(4, 1, 3), 2) HE(v(4, 1, 3), 3) H(v(4, 1, 3)) 3bit codebook 2 antennas, H(v(2, 1, 6)) 6 bit codebook 3 antennas,HC(v(3, 1, 3), v(2, 1, 3)) HC(v(3, 1, 3), H(v(2, 1, 3))) 6 bit codebook4 antennas, HC(v(4, 1, 3), v(3, 1, 3)) HE(v(4, 1, 6), 3) H(v(4, 1, 6)) 6bit codebook 3 antennas, HC(v(3, 1, 6), v(2, 1, 3)) HC(v(3, 1, 6),H(v(2, 1, 3))) 9 bit codebook 4 antennas, HC(v(4, 1, 6), v(3, 1, 3))HC(v(4, 1, 3), HC(v(3, 1, 3), v(2, 1, 3))) HC(v(4, 1, 3), HC(v(3, 1, 3),H(v(2, 1, 3)))) 9 bit codebookThe set notation v(N_(t), N_(s), L) in the input parameter of theoperations (i.e. H, HC, and HE) denotes that each matrix/vector in thecodebook v(N_(t), N_(s), L) is sequentially taken as an input parameterto the operations. The feedback index is constructed by concatenatingall the indexes s of the input argument vector codebooks in binaryformat. For example, the feedback index of HC(v(4,1,6), v(3,1,3)) isconstructed as i₂j₂, where i₂ and j₂ are the indexes of the vectors incodebook v(4,1,6) and v(3,1,3) in binary format respectively.Index Property:

According to one example embodiment, for the codebooks generated from HCoperation, their indexes are formed by the concatenation of the indexesfor the constituent codebooks. For example, the 4 by 2 6 bit codebook isformed by the concatenation of a 4 by 1 3 bit codebook and a 3 by 1 3bit codebook. The 6 bit index of the 4 by 2 6 bit codebook can bedivided into two portions. Namely, the first 3 bits are the index forthe constituent 4 by 1 vector codebook, which determines the firstcolumn of the 4 by 2 beamforming matrix, and the last 3 bits are theindex for the 3 by 1 vector codebook, which determines the second columnof the beamforming matrix jointly with the first 3 bits.

The importance of the beamforming matrix columns usually decreases thecolumn index because the column with a smaller column index correspondsto an eigenmode (or spatial channel) with a greater channel gain. Theconcatenation property of the index enables a scalable feedback. Forexample, we may feed back only the first few bits if there is not enoughfeedback bandwidth. For another example, we may assign differentprotections to the bits for different columns. For the third example, wemay feed back the index for the first columns more often than those forthe latter columns.

Reduction of Peak to Average Power Ratio (PAR)

The peak to average power ratio (PAR) is defined as

$\begin{matrix}{{{PAR} = \frac{\max\limits_{t}{x_{i,t}}^{2}}{E_{t}\lbrack {x_{i,t}}^{2} \rbrack}},} & (5)\end{matrix}$where X_(i,t) is the transmitted real signal on the i-th antenna at timeinstant t in time domain; the maximization and expectation are overtime. It is desirable to reduce PAR to reduce the corresponding effectof transmission signal distortion in power amplifier. In developing thecodebooks derived in, e.g., Tables 1-5, the effective PAR was not adesign consideration and, in that regard, the resultant codebooks maynot be designed to reduce (perhaps to a minimum), or limit the PAR. Forexample, codeword [1 0 0]^(T) is optimized for storage memory but notPAR reduction as all of the transmission power is allocated on the firstpower amplifier.

According to one example embodiment, CGA 108 may generate a codebookwith improved PAR performance than those generated according to thetechniques introduced above. In particular, CGA 108 may process one ormore codeword matrix(es) associated with a codebook (e.g., such as onegenerated in accordance with the techniques introduced above) togenerate a modified codeword matrix with improved PAR performancecharacteristics (e.g., reduced PAR) when compared to the originalcodeword matrix. According to one embodiment, CGA 108 may improve theeffective PAR on a give codebook by applying one or more, e.g., two,unitary transformations Q_(C) and P_(C) to a given codebook as{tilde over (V)}=Q _(C) V P _(C),   (6)where V is the codeword matrix in codebook C of dimension N_(t) byN_(s); Q_(C) is a complex unitary matrix of dimension N_(t) by N_(t) andit is constant for the whole codebook C; P_(C) is a complex unitarymatrix of dimension N_(s) by N_(s) and it is constant for the wholecodebook C; {tilde over (V)} is the processed codeword matrix withimproved PAR characteristics.

According to one example embodiment P_(C) is implemented as the identitymatrix and, since the unitary transformation Q_(C) conducts a rotationon the whole codebook C, the rotated codebook {tilde over (C)} has thesame structure (i.e. relative distances between codewords) as theoriginal codebook C. Furthermore, for any unitary matrixes P_(C) andQ_(C), it can be shown that the distance between any two codewords V₁and V₂ in codebook C is exactly the same as that between thecorresponding codewords {tilde over (V)}₁ and {tilde over (V)}₂ incodebook {tilde over (C)}, where {tilde over (V)}₁=Q_(C) V₁ P_(C) and{tilde over (V)}₂=Q_(C) V₂ P_(C). This implies that the transformedcodebook {tilde over (C)} has the same structure as the originalcodebook C. In this regard, the PAR performance can be improved byidentifying and utilizing unitary transformations Q_(C) and P_(C) thatreduce the PAR (perhaps to a minimum). The numbers of the effectivedegrees of freedom of Q_(C) and P_(C) are N_(t) (N_(t)−1) and N_(s)(N_(s)−1) respectively.

In an OFDM system, for example, searching for appropriate Q_(C) andP_(C) to reduce, e.g., to a minimum, the PAR using the definition inequation (5) may be difficult, as the signal is in the time domain andthe signal is the superposition of multiple sinusoids carrying data.Furthermore, the search results may vary with the OFDM parameters suchas the number of subcarriers and the bandwidth. Accordingly, twocriteria (perhaps sub-optimal) are derived for the searching, whichfocus the search for one subcarrier. The first criterion seeks to reduce(e.g., to a minimum) a maximum peak value, while the second criterionseeks to reduce (e.g., perhaps to a minimum) the mean power as shown in(7) and (8) respectively.

$\begin{matrix}{{\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\frac{\max\limits_{{V \in C},i}( {\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}} )^{2}}{\underset{{V \in C},i}{E}{\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}^{2}}}}};} & (7) \\{{\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\frac{\max\limits_{{V \in C},i}{\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}^{2}}}{\underset{{V \in C},i}{E}{\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}^{2}}}}};} & (8)\end{matrix}$where {tilde over (V)}=Q V P; {tilde over (v)}_(i,j) denotes the entryof {tilde over (V)} on the i-th row and j-th column and its is thesignal from one subcarrier among the superposition of all subcarriers;the maximization in the numerator and the expectation in the denominatorare over the rows of {tilde over (V)} and all codeword {tilde over (V)}in the rotated codebook {tilde over (C)}. Since the denominator in (7)and (8) is a constant independent of Q and P, equation (7) and (8) canbe rewritten as

$\begin{matrix}{{\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}( {\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}} )^{2}}}},} & (9) \\{\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{\sum\limits_{j = 1}^{N_{s}}{{{\overset{\sim}{v}}_{i,j}}^{2}.}}}}} & (10)\end{matrix}$

For systems employing high order QAM such as 64 QAM, the transformationP_(C) provides little help and thus can be dropped. In this regard,expression (9) and (10) can be simplified as

$\begin{matrix}{{Q_{C} = {\underset{Q}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}( {\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}} )^{2}}}},} & (11) \\{{Q_{C} = {\underset{Q}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}^{2}}}}},} & (12)\end{matrix}$where {tilde over (V)}=Q V.Performance Analysis

Turning briefly to FIG. 3, a graphical representation of the performanceimprovements achieved through use of the codebook generation agent isdepicted, according to one embodiment of the invention. The proposedcodebook generation techniques were simulated and compared toconventional techniques. The frequency permutation is Band AMC in802.16e D5 standard. ITU Pedestrian B, LOS channel model with 0.2transmit antenna correlation is employed. Perfect channel estimation andslow speed are assumed. The amount of feedback from the mobile device(e.g., 106) to the base station (e.g., 102) is 6 bits per AMC band. Withreference to FIG. 3, the feedback is the codebook index pointing amatrix codeword in a 64-codeword codebook. Packet error rate (PER) atthe downlink is simulated, where packet size is 1000 bytes. As shown inFIG. 3, the simulation results demonstrate that the proposedtechnique(s) 302 provide similar or better performance with much lowerstorage complexities than conventional technique(s) 304.

Having introduced the communication environment and operatingcharacteristics of CGA 108 with respect to FIGS. 1 and 2, above,reference is now directed to FIG. 4 which provides an example electronicdevice architecture within which the CGA 108 may be practiced.

FIG. 4 illustrates a block diagram of an example architecture of anelectronic device within which the teachings of the present inventionmay be practiced, according to one embodiment. Electronic device 400includes antennas, physical layer (PHY) 402, media access control (MAC)layer 404, network interface(s) 406, processor(s) 408, and memory 410.In some embodiments, electronic device 400 may be a station capable ofgenerating one or more matrix codebook(s) from matrix codeword(s)dynamically generated from vector codebook(s) for 2, 3, 4, . . . N-unitvectors by selectively performing Householder transformations asdescribed above. In other embodiments, electronic device 400 may be astation that receives feedback index, and performs beamforming in a MIMOsystem. For example, electronic device 400 may be utilized in a wirelessnetwork as station 102 or station 104 (FIG. 1). Also for example,electronic device 400 may be a station capable of performing thecalculations shown in any of the equations above.

In some embodiments, electronic device 400 may represent a system thatincludes an access point, a mobile station, a base station, or asubscriber unit as well as other circuits. For example, in someembodiments, electronic device 400 may be a computer, such as a personalcomputer, a workstation, or the like, that includes an access point ormobile station as a peripheral or as an integrated unit. Further,electronic device 400 may include a series of access points that arecoupled together in a network.

In operation, device 400 may send and receive signals using one or moreof the antennas, wherein the signals are processed by the variouselements shown in FIG. 4. As used herein, the antennae may be an antennaarray or any type of antenna structure that supports MIMO processing.Device 400 may operate in partial compliance with, or in completecompliance with, a wireless network standard such as, e.g., the 802.11or 802.16 standards introduced above.

Physical layer (PHY) 402 is selectively coupled to one or more of theantennae to interact with a wireless network. PHY 402 may includecircuitry to support the transmission and reception of radio frequency(RF) signals. For example, in some embodiments, PHY 402 may include anRF receiver to receive signals and perform “front end” processing suchas low noise amplification (LNA), filtering, frequency conversion or thelike. Further, in some embodiments, PHY 402 may include transformmechanisms and beamforming circuitry to support MIMO signal processing.Also for example, in some embodiments, PHY 402 may include circuits tosupport frequency up-conversion, and an RF transmitter.

Media access control (MAC) layer 404 may be any suitable media accesscontrol layer implementation. For example, MAC 404 may be implemented insoftware, or hardware or any combination thereof. In some embodiments, aportion of MAC 540 may be implemented in hardware, and a portion may beimplemented in software that is executed by processor 408. Further, MAC404 may include a processor separate from processor 408.

In operation, processor 408 may read instructions and data from memory410 and perform actions in response thereto. For example, processor 408may access instructions from memory 410 and perform method embodimentsof the present invention, such as method 200 (FIG. 2) or other methodsdescribed herein. In this regard, processor 408 is intended to representany type of processor, including but not limited to, a microprocessor, adigital signal processor, a microcontroller, or the like.

Memory 410 represents an article that includes a machine readablemedium. For example, memory 410 represents a random access memory (RAM),dynamic random access memory (DRAM), static random access memory (SRAM),read only memory (ROM), flash memory, or any other type of article thatincludes a medium readable by processor 408. Memory 410 may storeinstructions for performing the execution of the various methodembodiments of the present invention. Memory 410 may also store vectorcodebooks of 2, 3, 4, . . . N-unit vectors, although the invention isnot limited in this respect.

Network interface 406 may provide communications between electronicdevice 400 and other systems. For example, in some embodiments,electronic device 400 may be an access point that utilizes networkinterface 406 to communicate with a wired network or to communicate withother access points. In some embodiments, electronic device 400 may be anetwork interface card (NIC) that communicates with a computer ornetwork using a bus or other type of port.

As used herein, embodiments of CGA 108 may well be implemented in one ormore of PHY 402, MAC 404, processor(s) 408, and/or combinations thereof.As introduced above, CGA 108 may well be implemented in hardware,software, firmware or combinations thereof.

Although the various elements of device 400 are depicted as disparateelements in FIG. 4, embodiments are envisioned that may combine one ormore elements, or that may contain more elements. For example, thecircuitry of processor 408, memory 410, network interface 406, and MAC404 may well be integrated into a single integrated circuit.Alternatively, memory 410 may be an internal memory within processor408, or may be a microprogram control store within processor 410. Insome embodiments, the various elements of device 400 may be separatelypackaged and mounted on a common circuit board. In other embodiments,the various elements are separate integrated circuit dice packagedtogether, such as in a multi-chip module, and in still furtherembodiments, various elements are on the same integrated circuit die.

Alternate Embodiment(s)

FIG. 5 illustrates a block diagram of an example storage mediumcomprising content which, when invoked, may cause an accessing machineto implement one or more aspects of the codebook generation agent 108and/or associated methods 300. In this regard, storage medium 500 mayinclude content 502 (e.g., instructions, data, or any combinationthereof) which, when executed, causes an accessing appliance toimplement one or more aspects of the codebook generation agent 262described above.

The machine-readable (storage) medium 500 may include, but is notlimited to, floppy diskettes, optical disks, CD-ROMs, andmagneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, magnet or opticalcards, flash memory, or other type of media/machine-readable mediumsuitable for storing electronic instructions. Moreover, the presentinvention may also be downloaded as a computer program product, whereinthe program may be transferred from a remote computer to a requestingcomputer by way of data signals embodied in a carrier wave or otherpropagation medium via a communication link (e.g., a modem, radio ornetwork connection). As used herein, all of such media is broadlyconsidered storage media.

It should be understood that embodiments of the present invention may beused in a variety of applications. Although the present invention is notlimited in this respect, the circuits disclosed herein may be used inmany apparatuses such as in the transmitters and receivers of a radiosystem. Radio systems intended to be included within the scope of thepresent invention include, by way of example only, wireless local areanetworks (WLAN) devices and wireless wide area network (WWAN) devicesincluding wireless network interface devices and network interface cards(NICs), base stations, access points (APs), gateways, bridges, hubs,cellular radiotelephone communication systems, satellite communicationsystems, two-way radio communication systems, one-way pagers, two-waypagers, personal communication systems (PCS), personal computers (PCs),personal digital assistants (PDAs), sensor networks, personal areanetworks (PANs) and the like, although the scope of the invention is notlimited in this respect. Such devices may well be employed within any ofa variety of

Embodiments of the present invention may also be included in integratedcircuit blocks referred to as core memory, cache memory, or other typesof memory that store electronic instructions to be executed by themicroprocessor or store data that may be used in arithmetic operations.In general, an embodiment using multistage domino logic in accordancewith the claimed subject matter may provide a benefit tomicroprocessors, and in particular, may be incorporated into an addressdecoder for a memory device. Note that the embodiments may be integratedinto radio systems or hand-held portable devices, especially whendevices depend on reduced power consumption. Thus, laptop computers,cellular radiotelephone communication systems, two-way radiocommunication systems, one-way pagers, two-way pagers, personalcommunication systems (PCS), personal digital assistants (PDA's),cameras and other products are intended to be included within the scopeof the present invention.

The present invention includes various operations. The operations of thepresent invention may be performed by hardware components, or may beembodied in machine-executable content (e.g., instructions), which maybe used to cause a general-purpose or special-purpose processor or logiccircuits programmed with the instructions to perform the operations.Alternatively, the operations may be performed by a combination ofhardware and software. Moreover, although the invention has beendescribed in the context of a computing appliance, those skilled in theart will appreciate that such functionality may well be embodied in anyof number of alternate embodiments such as, for example, integratedwithin a communication appliance (e.g., a cellular telephone).

In the description above, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form. Any number ofvariations of the inventive concept are anticipated within the scope andspirit of the present invention. In this regard, the particularillustrated example embodiments are not provided to limit the inventionbut merely to illustrate it. Thus, the scope of the present invention isnot to be determined by the specific examples provided above but only bythe plain language of the following claims.

1. A computer-implemented method comprising: processing each codewordmatrix associated with a codebook to generate a modified codebook withan improved peak to average power ratio (PAR) as compared to thecodebook; and sending beamforming feedback to a remote device, thebeamforming feedback based on the modified codebook.
 2. A methodaccording to claim 1, the element of processing comprising: applying atleast one of two unitary transformations Q_(C) and P_(C) to a givencodebook according to {tilde over (V)}=Q_(C) VP_(C), where V is thecodeword matrix in codebook C of dimension N_(t) by N_(s), Q_(C) andP_(C) are complex unitary matrices of dimensions N_(t) by N_(t) andN_(s) by N_(s) respectively and are constant for an entirety of codebookC.
 3. A method according to claim 2, wherein one or more of Q_(C) andP_(C) are derived according to at least one of$\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{( {\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}} )^{2}\mspace{14mu}{and}}}}$$\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{\sum\limits_{j = 1}^{N_{s}}{{{\overset{\sim}{v}}_{i,j}}^{2}.}}}}$4. The method of claim 1; wherein the improved PAR comprises a reducedPAR as compared to the codebook.
 5. An apparatus, comprising: a codebookgeneration agent, to process each codeword matrix associated with acodebook to generate a modified codebook with an improved peak toaverage power ratio (PAR) as compared to the codebook; and a transceiverto send beamforming feedback to a remote device, the beamformingfeedback based on the modified codebook.
 6. An apparatus according toclaim 5, wherein the codebook generation agent selectively applies atleast one of two unitary transformations Q_(C) and P_(C) to a givencodebook according to {tilde over (V)}=Q_(C) V P_(C), where V is thecodeword matrix in codebook C of dimension N_(t) by N_(s), Q_(C) andP_(C) are complex unitary matrices of dimensions N_(t) by N_(t) andN_(s) by N_(s) respectively and are constant for an entirety of codebookC.
 7. An apparatus according to claim 6, wherein the codebook generationagent selectively derives at least one of$\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{( {\sum\limits_{j = 1}^{N_{s}}{{\overset{\sim}{v}}_{i,j}}} )^{2}\mspace{14mu}{and}}}}$$\{ {Q_{C},P_{C}} \} = {\underset{Q,P}{argmin}\mspace{14mu}{\max\limits_{{V \in C},i}{\sum\limits_{j = 1}^{N_{s}}{{{\overset{\sim}{v}}_{i,j}}^{2}.}}}}$8. The apparatus of claim 5; wherein the improved PAR comprises areduced PAR as compared to the codebook.
 9. An apparatus, comprising: amemory including data representing a codebook of one or more codewordmatrix(es); and a codebook generation agent, coupled to the memory, toprocess each codeword matrix associated with the codebook to generate amodified codebook with an improved peak to average power ratio (PAR) ascompared to the codebook; and a transceiver to send beamforming feedbackto a remote device, the beamforming feedback based on the modifiedcodebook.
 10. The apparatus of claim 9; wherein the improved PARcomprises a reduced PAR as compared to the codebook.